eee 27 F726 L 


AN INQUIRY 
ye FC) VA MORE PERFECT FORM 


OF 


WATER-WHEEL 


BY 


J. P. FRIZELL 
| i. 


BOSTON 
60 CONGRESS STREET 
1897 


tga. 





pe? oo Se arc 


‘Boker, ; s 


‘ Tro - 





An Inquiry ase toma 


More Perfect Form of Water-Wheel 


A WATER-WHEEL is a wheel for applying the power of water to 
some useful purpose. 

Water-power implies two things: a flow of water and a fall. 
We will express the former generally by the symbol g in cubic feet 
per second, the latter by h in feet. 

Work is mechanical effect. It implies resistance overcome, and is 
conveniently represented by the raising of a weight. <A pressure of 
1 pound overcome through a distance of 1 foot is equivalent to the 
raising of a pound one foot and is called a foot-pound. 550 foot- 
pounds per second is a horsepower. ‘The weight of a cubic foot of 
water at ordinary temperatures is very nearly 622 Ibs. It varies 
slightly with the temperature, and will be here represented by the 
letter w. In computations relative to water-power, w is usually 
taken at 62.5 pounds. Another symbol of frequent use in hydraulie 
computations is the velocity imparted per second by gravity, desig- 
nated by the letter g. This varies slightly with the latitude and 
altitude of the place. 

Energy is capacity to perform work. <A quantity g of water in a 
mill-pond, at a height # above the tail-water, has the energy wqh 
foot-pounds, and it could exert that amount of energy if we neglect 
the losses incident to the application. A quantity ¢ of water at the 
level of the tail-water, supposing it enclosed in a penstock communi- 
eating with the head-water, could exert upon a piston of 1 square 
foot cross-section the pressure wh pounds, and could move the piston 
q feet, representing an amount of energy of wqh foot-pounds. En- 

ergy in these forms is called potential energy, being the energy of 
position or the energy of pressure. When water, in the last named | 
3 


4 A More Perfect Form of Water - Wheel. 


case, issues from an orifice at or below the level of the tail-water, it 


9 


Oe y 
takes a velocity, v = 2gh, and its energy is wq ino wah. This 


form of energy is called kinetic energy, or the energy of velocity. 

Two remarks of importance may be here made as bearing on what 
follows : — 

1. A head of water can exert a pressure or generate a velocity, 
but it cannot increase one of these effects without diminishing the 
other. When it has its full effect of pressure it can produce no veloc- 
ity. When it has its full effect of velocity it can exert no pressure. 
This, of course, implies that the velocity is directly communicated 










































































by the pressure. Water under pressure may be put in motion by an 
extraneous cause without any effect upon the pressure. 

2. The energy with which water leaves a hydraulic motor is a de- 
duction from the efficiency of the motor. 

The efficiency of a wheel is its energy as compared with the energy 
of the water acting on it. 

A wheel which could raise the water that acts on it to the full 
height of the fall would have perfect efficiency in the organs by 
which it is acted on as well as in the organs by which it acts. We 
know this to be a mechanical impossibility, by reason of the natural 
resistances to motion. We should regard it as a very perfect appa- 
ratus that could perform this duty with an efficiency of 70 per cent. 
Nature, however, accomplishes the same result with an efficiency of 
more than 99 per cent. Consider the system of pipes represented in 
Fig. 1. Suppose the pipes a and b to be 20 feet in length. Water 


AW More Perfect Form of Water - Wheel. 5 


goes down @ and rises through b. The descent of the water in a 
may be regarded as the motive power; its elevation through 0 as the 
effect produced. A difference of one inch on opposite sides of the 
partition ¢ will cause a perceptible current through the pipes. This 
machine acts with an efficiency of 99.6 per cent. 
Water acts to turn a wheel in three ways : — 
1. By weight. 
2. By impulse. 
3. By reaction. 
The first is exemplified in the now nearly obsolete forms of over- 
shot and breast wheels, which it is not our present purpose to discuss. 
The action of water by impulse depends upon certain well-known 
mechanical principles. Force is required to impart velocity to water, 
Cc 


Fig. 2 


and the velocity imparted is a correct measure of the force employed 
in imparting it. When water is in motion, force is required to change 
the direction or velocity of its motion, and the change of motion is a 
correct measure of the force. Suppose, for instance, a jet of water, 
moving from D toward B, in the line DAB. At A it encounters a 
smooth vane which so deflects it that it reaches C instead of B, at 
the end of one second, A B representing the velocity of the jet, BC 
is the change of motion occasioned by the vane. ‘The effect of the 
vane is to impart to the water a velocity BC, and the pressure on 
the vane is in a direction parallel to CB. To find the pressure of 
the water on the vane, which is equal and opposite to that of the 
vane upon the water, we reason thus : — 

Gravity acting freely for one second would impart to the water a 
velocity of g feet per second. The pressure of the vane acting for 
one second imparts to the water a velocity BC per second. There- 
fore, the pressure on the vane is to the weight of water flowing in 
one second as BC is tog. If a@ represents the cross-section of the 


; BC 
stream, the weight of water is-wav, and the pressure is wav 





6 A More Perfect Form of Water - Wheel. 


pounds. This is the pressure in the direction BC. To find the 
normal pressure we should use, instead of BC, its projection on a 
line perpendicular to the vane. 

The impulse of water upon a stationary vane is attended with no 
material loss of energy. The water glides along the vane and glances 
off at the extremity, in a direction tangent to the latter, with sub- | 
stantially undiminished velocity. When the vane moves under the 
action of the water, a portion of the energy is imparted to the vane, 
and the energy of the stream is correspondingly diminished. It is 
manifest that if the energy of the stream is wholly imparted to the 
vane, it must leave the latter with no absolute velocity. That is, its 
velocity must be equal and opposite to that of the vane at the point 
of exit. 





Fig. 3 


Let us now consider the action of a jet on a flat vane perpendicu- 
lar to its direction and moving in the same direction as the jet. In 
Fig. 3, let BC=v represent the original direction and velocity of the 
jet, B D = u the velocity of the vane. Were the vane not present, a 
particle of water at B would have reached C at the end of one sec- 
ond. By the action of the vane, the particle finds itself at the point 
A, at the end of one second, ) A being =v—wu. AC is the change 
of motion due to the action of the vane. ‘The pressure on the vane, 


hee aA CE Sen ; 
in a direction parallel to 4 C, is wav ——. The change of motion 
4 


normal to the vane is DC. ‘The normal pressure on the vane is 





D Di a 
P=wav —=wav (1) 
y g 
The energy imparted to the vane is 
UAV — Ww) 
Pas PAO (2) 


Y 


A More Perfect Form of Water - Wheel. 7 


This expression has its maximum value when wu = $v, and becomes 
in that case 
aes 
Pu=fF wav ——4wavh (3) 
29 
h being the head to which the velocity is due. In other words, the 
maximum energy that can be imparted to a flat vane normal to the 
stream is one-half that of the stream, or the maximum efficiency is 
50 per cent, and the best velocity for such a vane is one-half that 
due the head. 
There are two cases in which the energy becomes 0, viz. : 
1. When w is 0, i.e. when the vane does not move. In that case, 


Eq. 1 spit eae (4) 


That is, the pressure on the vane is twice that of the head to which 
the velocity is due. 





Pg. +4} 


2. When u = v, that is, when the velocity of the vane is equal to 
that of the stream. 

A cup-shaped vane, Fig. 4, reverses the direction of the water’s 
motion; so that if such a vane be moving in the direction of the 
stream with a velocity u, the change of motion will be 2 (v— w). 


2(v—u 
Paw OV geen ls (5) 
y) 
And the energy exerted on the vane is 
Dab Ul 
Pu=wav ace a Pe (6) 
g 


As before, the expression has its maximum value when v = 2 u, 
in which case 


9 


PUES wav y=" avh. (7) 
Or the total energy of the stream is imparted to the vane, and the 
efficiency is 100 per cent. We have proceeded, however, upon as- 
sumptions which cannot be perfectly realized. In any practical appli- 
cation the direction of the water’s. motion cannot be exactly reversed, 
the vanes and their attachments cannot move without friction, the 


8 A More Perfect Form of Water - Wheel. 


water cannot approach and leave the vanes without velocity and con- 
sequent loss of head. The practical interpretation of this result is, 
that the arrangement described is consistent with the highest effi- 


ciency. Equation 5 shows that when the vane does not, move, the 
pressure 


. qs 2 


Gas ea eae 9° (8) 


cy 


That is, the pressure on the vane is four times that of the head to 
which the velocity is due. As in the former case, the energy be- 
comes 0 when vu = 0, and when wv = v. 

To trace the application of the above principles to different forms 
of vanes, and to vanes which do not move in the same line as the 
water, would be foreign to our present purpose, which is merely to 
put the reader in a position to understand what follows. We are, 
nevertheless, even now, in a position to notice two points of impor- 
tance which are commonly lost sight of in the design of water- 
wheels : — 

1. The purpose of the vanes or floats in an impulse wheel is to 
effect the greatest possible change in the motion of the water. Their 
length need be no greater than is necessary to accomplish that 
change. 

2. It is a condition of the highest efficiency that the water should 
leave the vane with a velocity equal and opposite to that of the vane 
at the point of exit. Where the edge of the vane is radial to the 
wheel, different parts of it move with different velocities, and the ful- 
fillment of this condition is impossible. 

Reaction is the pressure exerted on the walls of a pipe or vessel 
from which water is discharged. Strictly speaking, the discharge of 
water from an orifice does not create pressure within the pipe or 
vessel from which it issues. It destroys the equilibrium of pressures 
previously existing. Suppose the pipe, Fig. 5, filled with water 
under pressure, and free to revolve around the center c. When the 
orifice o is closed, there is no tendency in the pipe to revolve. The 
water presses equally upon every part of the interior, and the force 
tending to turn it toward the right is exactly balanced by that tend- 
ing to turn it toward the left. When the orifice 0 is opened, the 
conditions are changed. ‘There is now a small space relieved of 
pressure on one side of the pipe, while the pressure acts in full force 
on the other side. The pipe will revolve around the center ¢ in a 
‘direction opposite that of the stream. 


A More Perfect Form of Water - Wheel. 9 


In the arrangement indicated by Fig. 6, water issues from the 
orifice o and impinges upon a flat vane or plate P, which is in a line 
with the center c. The pipe in this case would have no tendency to 
revolve, as is evident from this consideration. In the arrangement 
of Fig. 5, the energy of the stream diminishes as the pipe revolves, 
u being the velocity of the orifice, and v that of the stream, the 
velocity relative to a fixed point will be v — uw, and the energy of the 


2 
Ou oi 
stream = Saat) wav. In the case of Fig. 6, the energy of the 
‘ 4 g ry 


re 





: Coa e we : 
water will be wav —,-—. That is to say, the energy of the stream 
* rp cc 


we 


must increase if the system revolves; so that, instead of developing 
























































Fig. 6 Fig. 5 


energy, a constant expenditure of energy would be required to keep 
it in motion. We do not here consider the centrifugal force devel- 
oped in the water when the pipe revolves... These considerations 
enable us to estimate the force of reaction. Since the system has no 
tendency to revolve, the reaction on the pipe must be exactly equal 
to the pressure on the vane. ‘This we have already found equal to 
2wah. Let Fig. 7 represent the rim of a wheel containing the 
orifices 00, so disposed as to discharge water in a direction, as 
nearly as may be, tangential to the wheel. We assume for our 
present purpose that the direction is absolutely tangential. Let a, 
as before, represent the cross-section of the stream. The water is 
supposed to be at a greater pressure within the wheel than without, 
the difference of pressure being represented by the head h. 

The best velocity of the circumference is that with which the water 


10 A More Perfect Form of Water - Wheel. 


issues, being the velocity due the head h. In this case, the absolute 
tangential velocity of the water leaving the wheel is o. 

The energy imparted to the wheel is 2 wa uh = twice the energy of 
the water under the given head. 

This does not imply that the wheel is capable of yielding an 
efficiency of 200 per cent. In order that the water may issue from 
the orifices while the wheel is in motion, it must receive a tangential 
velocity equal to that of the wheel. To impart this velocity requires 
the energy wavh. The wheel then, under the conditions supposed, 
is capable of exciting the energ 


2wavh—wavh=wavh 





Fig 8 





and from this must be deducted the several losses incident to motion, 
together with that due to the deviation of the issuing stream from the 
direction of a tangent. 

In the above illustration of the principle of reaction no account is 
taken of the effect of the centrifugal force developed by the whirling 
motion of the water. The introduction of this element makes the 
problem more complex. The full effect of centrifugal force appears 
in the arrangement of Fig. 5,.in which a pipe filled with water, under 
pressure, revolves around a center ¢, discharging from an orifice 0, 
the entire mass of water being in rotation with uniform angular 


A More Perfect Form of Water - Wheel. 11 


velocity. This principle is demonstrated later on: — If we give the 
orifice o a velocity, v = u = V2gh, we develop at any point in the 
whirling mass of water a centrifugal force equal to the force repre- 
sented by the head due the velocity at that point. The pressure 
acting on the orifice under this condition will be 2wah, and the 
velocity of the discharge will increase to v= Y2q K 2h=1.4143 
V2gh. If we increase the velocity wu of the orifice so as to make 
u = 1.4143 29h, we develop a still greater centrifugal force, and so 
on. So that the condition of maximum efficiency v = — wu is impos- 
sible. 

If, for example, we attempt to determine the value of uw on the 
assumption that it is equal to the velocity with which the water issues 
from the orifice 0, we should have the equation 


he 
waaf2g (ht —) 
29 


or u?= 2gh + u?, which is only possible when h =o. 
In the arrangement of Fig. 7 the entire mass of water is not set in 
motion with uniform angular velocity from the center outwards, and 


the pressure head developed by centrifugal force is less than that due 
u? 

the velocity of rotation. Suppose it to be represented by coon 
Y 


2 





being less than unity. 
In this case 


= 42 eet 
Uu= g (h 29 


when u?=2gh+ mu? and 





The fulfillment of the condition » = — uw would be possible in such 
a wheel, but w would be so great that the losses from friction and 
resistance to motion would exceed the waste of energy incident to a 
lower velocity. 

A wheel of the form indicated at Fig. 8 would operate wholly by 
reaction. The water within the wheel would have a whirling motion, 
the tangential component of which is equal to the velocity of the 
inner circumference. We know this because otherwise the water 
could not enter the wheel. This whirling motion is not the direct 
effect of the head. It is imparted to the water mechanically by the 


12 A More Perfect Form of Water - Wheel. 


wheel. The pressure of the water does not diminish till the latter has 
entered the buckets. The energy of reaction exerted at the orifices of 
discharge exceeds the total energy due the head. ‘This, as we have 
already seen, is partly absorbed in imparting the whirling motion to 
the water before it enters the wheel. 

Impulse and Reaction Wheels. —- Most wheels act partly by im- 
pulse and partly by reaction. In a wheel acting purely by impulse 
the water issues from orifices with the full velocity due the head and 
impinges upon vanes moving, preferably, with half that velocity. In 
a purely reaction wheel the work of the water is finished when it 
issues from the orifices of discharge. A tangential velocity equal to 
that of the influx orifice is imparted to the water, not directly by the 
head, but indirectly through the action of the wheel. Neglecting 

friction and losses incident to the movement of the water, the energy 

“imparted to the wheel by the water is twice that due the head and 
quantity, but of this, one-half or more is useless energy, being that 
expended in imparting the necessary tangential movement to the 
water. 

A wheel which has found many useful applications in cases of high 
head and small flow is the Pelton or hurdy-gurdy wheel. A jet of 
water acts upon cup-shaped vanes (Fig. 4) disposed around the 
circumference of the wheel. ‘This is an impulse wheel pure and _ 
simple. The Barker Mill (Fig. 5) and the forms of Figs. 7 and 8 
are reaction wheels pure and simple, observing that in 5 and 7 the 
orifices of influx and discharge are the same. 

All wheels with guides may be regarded as acting partly by impulse 

and partly by reaction. ‘The tangential velocity of influx is imparted 
directly by the head. The velocity of the efflux orifices is less than 
that due the head and greater than half the same. At full discharge 
they have more the character of reaction wheels. At diminished 
discharge they become impulse wheels. 
+ Impulse and reaction wheels have this in common: Their effi- 
ciency depends upon the change which they effect in the direction of 
the water’s motion, perfect efficiency implying exact reversal. Perfect 
efficiency also requires the water to leave the wheel with no tangen- 
tial velocity, a condition inconsistent with radial orifices of dis- 
charge. 

Centrifugal Force. — We shall have occasion in what follows to 
refer to certain propositions relative to the action of centrifugal force 
‘in the proposed form of wheel. I give in this place the demonstra- 


AW More Perfect Form of Water - Wheel. 13 


tion of these propositions so far as required for our purpose. It is 
impossible to set forth and demonstrate these propositions without 
the aid of mathematical symbols and operations which are only 
intelligible to those who have studied that subject. Those who have 
not must ask the advice of those who have, or else take the results 
upon trust. 

A cylindrical vessel, open at the top and partly filled with water, 
revolves around its vertical axis. What form will the surface as- 
sume ? 

Let Fig. 9 represent the vertical section of such a vessel. 

The ordinates of any point o, in the curve, are x= AD and 
y= Do; ow is the angular velocity. The surface must take such a 
form that the resultant of the forces acting at o will be normal to the 
surface. 





Fig..9 


The forces acting upon any given small mass, whose weight is w, 


. TO 
at o, are: vertical w, horizontal — wy. If we take y to represent 
J 


the centrifugal force, i.e. the horizontal force, then 2 will represent 
W 
the vertical force, and the forces acting at o may be represented by 
a) O,and =f = Fo=cD. The resultant of these two forces will 
W 


be represented by co, which must be normal to the surface. Now 


a = cD is independent of the position of o. In other words, the 
W@W 


subnormal is constant, which is a characteristic of the parabola. 
Any vertical section of the surface through the axis, therefore, is a 
parabola. 

The equation of the parabola referred to its axis and vertex is 
ordinarily written, 
Thee ted Ga (9) 
2 P being the value of « when 7 = y. 


14 A More Perfect Form of Water - Wheel. 








Stee Bee ; . Cy tla 
Differentiating (9) 2y¥dy=2 Pda, whence = =-—. The sub- 
wv y 
bd d Y ry. q e 
normal is 7¥ “=P, Therefore P—-—,, and the equation of the 
7 w~ 
curve may be put in the form 
ses 10) 
a 
24 ( 


wy? is the velocity of rotation at 0; therefore, at any point in the 
vessel, the height of the surface above its lowest point is the height 
due the velocity of rotation. 

The quantity of water in the cylinder remaining constant, and the 
cylinder being supposed of indefinite height, the rotation will not 
alter the aggregate pressure on the bottom, which is the weight of 
the liquid. ‘The rotation will only alter the distribution of the 
pressure. 

The question often arises, What is the pressure on the ends of a 
filled cylinder in rotation? Referring to Fig. 9, suppose, at the 
lowest point of the curved surface, a horizontal diaphragm ab to be 
inserted, forming a closed cylindrical vessel abcd. ‘The pressure 
on both sides of the diaphragm will be equal, that is, the centrifugal 
force developed in the mass below the diaphragm will be exactly 
equal to the weight of water above it. The water will be the con- 
tents of the cylinder /mba, less the contents of the paraboloid 
1Am. The volume of a paraboloid is one-half that of the cireum- 
scribing cylinder. The pressure on « b, therefore, is $7 wX a A®?Xal. 


Putting + for the radius of the cylinder, the pressure on ab is 
w- y2 

4warr? oe being the weight of a cylinder of water of radius 7, 

2 2y 


and height equal to one-half the head due the velocity of the exte- 
rior circumference. It must be observed that the effect of atmos- 
pheric pressure is not here considered. 

A vessel filled to the height H, the radius being 7, is set in motion 
with the angular velocity ». ‘To find the highest and lowest points 
of the water. 

The total volume of the water is 77? 77; ditto of the paraboloid, 





a = aa Late eethe height of the lowest point in the surface of 
: | 
w- y? 





water above the bottom of the vessel. Then 77? (a+ 4 aa 


= 71? H, whence 


A More Perfect Form of Water - Wheel. 15 





(11) 


2 2 
Ww”) 


yy 


il 
e 


The highest point of the surface will be at a height above the 











2 mr2 
lowest point, or at a height # + 3 : above the bottom. Its height 
above the bottom will be 
w- yr? 
= Tye. (12) 


ae 


Suppose the vessel abcd revolving around a horizontal axis, and 
it is required to find the pressure on the ends. We must remember 
that the centrifugal force developed in any particle of water is in no 
way affected by the direction of the axis of rotation, and will be the 
same as before. To this must be added the pressure due to the 
weight of the water in the cylinder. The surfaces on which the 
water acts are each r7?. The average static head, in the horizon- 
tal position of the axis, is7. This part of the pressure will be w77°, 
and the total pressure | 

Mar? (es th) (13) 


h being the head due the velocity at the exterior circumference. ‘The 
same result is obtained in a more direct manner, as follows. Put R 
for the exterior radius of the cylinder, and 7 for the distance, from 
the axis, of any point under consideration. ‘The centrifugal force, 


at any point, is 7° 7. This is the force with which a cubic foot of 


water pulls away from the center. The actual mass of water to 
which this applies is wh2a7rdvr, 6 being the axial length of the 
warrbar w 


cylinder. The force per square foot is — ———_— w?r =— o’ rdr. 
Gem U0 g 


This.is the pressure which the particles at a distance + from the axis 
of rotation exert on all the surface outside of them. The end sur- 
face on which this pressure takes effect is (??— 7°). The total 
pressure therefore due to centrifugal force is 


rR 
a of 1) (liao. Or 7, 
O 





where A is the area of the end of the cylinder. 


16 A More Perfect Form of Water - Wheel. 


Adding the pressure due to the weight of the water, we have for 
the total end pressure 
om Fe (hi hy, (14) 


the same result as before, putting / in the place of r. 

We are now prepared to consider the special question which will 
arise later, viz.: A cylindrical vessel in rotation, immersed in water, 
discharges water through a small orifice in its exterior circumference. 
What will be the pressure on the ends, from without inward? 

First, suppose the axis of rotation vertical, and let d be the depth 
of water on the upper end of the cylinder. Let P be the pressure of 
the atmosphere in pounds per square foot. Then the total downward 
pressure on the upper end of the cylinder is tr? (P+wd). The up- 
ward pressure per square foot at the outer circumference is P + dw, 


2.9 


“a 4s 


@ . 
and at the center P+ dw— ay w. ‘The pressure varies from the 


« 


center outward, according to the parabolic law. ‘The aggregate up- 
, h 
ward pressure is, therefore, 77? (P+ wd — Ws ), h being the head 


due the velocity of the exterior circle, and the effective pressure act- 


ing downward is 
= tar wits (15) 


The effective upward pressure on the lower end will be the same, 
being increased by the pressure due to the height of the vessel, and 
diminished by the weight of water in the vessel. 

Next, suppose the axis of rotation to be horizontal, and let d rep- 
resent the depth of the axis below the surface of the water. The 
depth of the orifice, while in rotation, will vary from d—r tod+7, 
its average depth being d. 

The pressure per square foot directed inward will be P + wd, the 
ageregate pressure being r7?(P+ wd). The pressure directed 
outward will be P+wd pounds per square foot at the circum- 


2 pad 


W@W 
ference, and P+ wd — at the center, the aggregate outward 


pel 
pressure being rr?>(P+wd—gwh). As before, the effective 
pressure tending to force the cylinder heads inward is $77? wh= 





h : ; 
mrws; that is to say, the pressure represented by one-half the 


in 


head due the velocity of the orifice. It appears that the orifice 
would play an important part in the pressure on such a revolving 


A More Perfect Form of Water - Wheel. 17 


h 
cylinder. If open, the pressure represented by . would act inward, 


if closed, outward. It is manifest that opening a larger orifice at 
the center of the cylinder would prevent the lowering of the pressure 
within the same, and have the same effect as closing the outer 
orifice, and the closing of the central orifice would have the same 
effect as opening the outer. 

This result would not hold if the velocity were so great as to make 
























































Pio 10 


h greater than the height due the atmospheric pressure increased by 
d, which would imply a vacuum at the center of the cylinder. 

It is not the purpose of this little essay to enter into a general de- 
scription of existing turbines. Some of their most prominent features, 
however, must be referred to in order to understand the advantages, 
if any, of the proposed form. 

Floats. — Figures 10, 11 and 12 may be taken as types of the 
existing form of floats. In Fig. 10 the letter f below the band 
denotes the same float as f above. ‘The water enters the wheel in a 
horizontal direction above the band and leaves it in an inclined 


18 A More Perfect Form of Water - Wheel. 


direction below. The orifices of discharge extend from the circum- 
ference nearly to the center. The same characteristics appear in 
ll and 12. ab, Fig. 11, is the length of the orifice of discharge, 
in a radial direction. The length of the passage traversed by the 
water appears clearly in 12. ‘These floats are at variance with both 
conditions of efficiency referred to on page 8. ‘They present a 
longer passage to the water than is necessary for the required change 
of direction. The orifices of discharge are radial, and, in Fig. 10, the 





inner end of the orifice moves with a velocity less than half that of 
the outer end; whereas, the velocity imparted to the water by the 
head acting on the wheel is substantially the same at the inner end 
as at the outer. The highest efficiency cannot be obtained from a 
wheel with floats of this form. The extent to which this form of | 
float affects the efficiency at full gate is not wholly a matter of 
conjecture or theory. The Boyden-Fourneyron wheel (Figs. 13, 14 
and 15), on the most rigorous trial, gave an efficiency of 88 per cent. 
The Swain wheel (Figs. 11, 12 and 16) has shown a maximum of 


A More Perfect Form of Water- W heel. 19 


85. This falling off of 3 points must be charged to the form of the 
floats. Wheel No. 10 is still more faulty in this respect. At a 
competition test at Holyoke several years ago, where a large number 
of wheels were entered for trial, this wheel gave, as a maximum, not 
quite 83 per cent. 

One maker of wheels —no doubt a very excellent mechanic and 
skillful man of affairs —says that the great power of his wheels 
‘* consists in the use of long buckets gradually leaning forward with- 
out any short or abrupt bend to prevent the natural flow or passage 
of water, and in turning the upper and outer half of the buckets 
forward in the direction the wheel runs, thus compelling the water 
that comes through the chutes to gather in largest bulk on the outer 





parts of the buckets and therefore exert more pressure because 


2 


pushing chiefly where there is most leverage.’’ This quotation shows 
how loose and vague are the ideas of the action of water entertained 
by makers of wheels. 

Guides. — Practically inseparable from every existing form of 
water-wheel are the guides for giving a suitable direction to the 
water entering the wheel. figures 13 and 14 show these parts as 
applied to the Boyden-Fourneyron Turbine, in which the water flows 


from within outward. They consist, here, in a series of thin steel 





blades inserted in the disc and forming a series of narrow and deep 
channels. In addition to their function of guiding the water, they are 
attached, at their upper outer corners, to the supply pipe, and serve 
the purpose of firmly uniting this part with the disc, a purpose which 


PAY AA More Perfect Form of Water - Wheel. 


it would. be impossible to secure in any other way without introducing 
parts that would interfere with the action of the water. It must be 
observed that the dise is an entirely indispensable part of the 
apparatus, serving to relieve the wheel and its bearings of the 
pressure of the water. In almost every form of center-vent wheel 
the guides sustain a plate through which the shaft passes in a stuffing- 
box and which serves, to relieve the wheel of pressure. ‘The point to 





Fig. 13 


which I wish to direct attention now, is this: The necessity of these 
parts to the structural solidity and strength of the wheel and case has 
diverted the attention of wheel-makers from the question: Are the 
guides necessary to the mechanical action of the wheel? 

In a wheel whose design and construction is otherwise consistent 
with the highest efficiency, it is possible to so adjust the angle of the 
guides, the opening of the guides and the discharge orifices of the 
wheel as to secure, at full gate, a high degree of efficiency. Nearly 
the highest that any wheel admits of. ‘This adjustment requires a 


A More Perfect Form of Water - Wheel. 21 


degree of knowledge of hydraulics that few men possess. But how- 
ever complete this adjustment may be at full gate, it begins to 
be deranged as soon as the gate begins to close and, generally, when 
the discharge is diminished one-half, is wholly destroyed, and the 
efficiency much reduced. Wheels of the form shown in Figs. 13, 14 and 
15 have shown, at full gate, the highest efficiency ever attained by : 
turbine. But observe how the conditions of efficiency are changed 
when the gate has descended to the position shown in Fig. 15. In 
this case, the water does not enter the wheel in the direction that the 


















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N NY IN ING 

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SANSass > 






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GAGBtAUE Ts 











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y 
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aT 


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SFISIGNS WA 


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Fig. 14 


ceuides would lead it. The opening formed by the gate and two 
consecutive guides is an orifice which the water approaches from 
various directions and from which it issues in a direction at right 
angles to the plane of the orifice, or radial to the wheel, at least 
tending to do so, and becoming so when the gate is nearly closed. 
The closing of the gate alters the direction of the water entering the 
wheel and so impairs its efficiency. But this is not the whole effect, 
nor the worst. The stream entering the bucket doesnot fill and pass 
smoothly through it as it does at full gate, but wastes its energy in 
commotions and eddies. It tends to fill the bucket at its exit, and so 
is discharged with a much lower velocity than it possessed at its 
entrance. . 


bo 
bo 


AA More Perfect Form of Water - Wheel. 


Here another remark might be offered as to the length of the 
passages through the wheel. ‘These, as before observed, need be no 
longer than will suffice to impart the necessary change of direction to 
the water. At part gate the portion of the passage not filled by the 
stream is filled with dead water. ‘The shorter the passage is, the less 
the stream mingles with the dead water, and the less the diminution 
of velocity sustained by it during its passage. ‘The longer the 
passages are, the more the stream expands in its passage, and the 
lower (up to the point where the stream completely fills the passage) 
will be the velocity of discharge. 











Yl hyp aps 


YW 






\y 





This is the inherent and unavoidable defect of the turbine: That 
it cannot use a diminished quantity of water with the same efficiency 
as the full quantity that it is fitted to discharge. A wheel which 
shows an efficiency of 88 per cent at full discharge generally shows 
not above 65 at half discharge, and below half it is so low that 
makers do not usually care to publish it. 

Nevertheless it is exceedingly desirable that water-wheels should 
be able to use a small quantity of water as efficiently as a large 
quantity. Streams vary constantly in flow. During several months 
in every year the flow of the stream is greatly below the capacity of 
the wheels. Steam is employed to make good the deficiency, and 
part gate is the normal condition of the wheels. It is extremely 
unfortunate that, at the period when water is the scarcest, it should 






A More Perfect Form of Water - Wheel. 23 


have to be used at a greatly diminished efficiency. The ability to 
work economically at $, + or even ¢ of full power is just as desirable 
in a water-wheel as in a steam-engine. 

Innumerable have been the devices for alleviating this defect. 
I would by no means attempt to describe or even name them. I will 
mention several of the most prominent. 



























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= 
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apse/ 
See! % ay 
3 nF Se y 
aoa 4 R Re aK 
ark SK 
N N N N 
N N N N 
N N N N 
N N N N 
N N N N 
N N Ny 
N N N NN 
N N N N 
N N N N 
N N N N 
N N N N 
N Ns Go SS \ \ 
N N S SS N 


Fig. 16 


1. In the wheel shown in Figures 13, 14 and 15, the guides have 
been given a sharp backward inclination, so as to stand at an angle 
of 45 degrees or less with the horizontal. In this arrangement a 
particle of water at the top of the guides, near the outer end, 
approaches the opening when the gate is low, not in a vertical, but in 
an inclined, direction, with a large component of tangential velocity. 
In a low position of the gate, however, the water does not reach the 
outlet of the guides with a suflicient velocity to overcome its tendency 
to issue in a radial direction. Moreover, this disposition does not 
affect the most serious source of loss, which is the tendency of the 


24 A More Perfect. Form of Water - Wheel. 


water to fill the orifices of discharge from the wheel, and issue there- 
from with a greatly diminished velocity. 

2. In the wheel just referred to, several horizontal partitions have 
been introduced separating the wheel into a number of compartments, 
or ‘* stories,” to prevent the stream from expanding during its pas- 
sage. This arrangement appears well calculated to diminish one 
source of loss incident to this form of wheel, but the results were not 
encouraging enough to lead to the extended adoption of this method. 
The tendency of the water to escape from the guides in a radial 
direction leads to losses of head which cannot be obviated by these 
means. In this condition of the wheel the guides cease to guide. 
Were the guides removed and the water allowed to enter the wheel 
entirely free from their control, there is reason to suppose that it 
would take a direction more conducive to efficiency. 

3. In the Swain wheel (Figures 11, 12 and 16) the guides are 
attached to a broad flange in the gate G, which closes by rising. As 
the gate rises, the guides enter an annular chamber above, which 
diminishes the free height of the guide passages in the same degree 
that it diminishes the opening of the gate. This appears to largely 
obviate the loss arising from a change of direction in the water 
entering the wheel at part gate, and greatly improves its action. 
Tests of this wheel have shown an efficiency of 85 at full discharge, 
60 to 70 at half, and some 45 at one-fourth of the full discharge. 
These results exceed any existing wheels on part gate, and are not 
inferior on full gate to any but that shown in Figures 13, 14 and 15, 
which has shown an authentic result of 88 per cent, and for which 
higher results have been claimed. The record of the Swain wheel, 
however, shows that there is still much to be desired in point of 
efficiency at part gate. It shows that this arrangement of gate does 
not obviate the second source of loss, viz. the expansion of the 
stream in traversing the buckets. 

4. Fig. 17 represents another attempt to use large and small 
quantities of water with good efticiency in the same wheel. This is 
nothing less than a double wheel, with two sets of floats, two sets of © 
cuides, and two gates, all on the same shaft. The outer wheel w w 
is governed by the cylindrical gate GG, which opens downward. 
The floats ff and guides yg belong to this wheel. ‘The inner wheel 
w' w' is controlled by the gate G’ G’, opening upwards, and has the 
cuides g/g’ and floats f’ f’. In times of abundant water both gates 
are open. In lower stages the inner gate is closed, leaving the outer 


A More Perfect Form of Water - Wheel. 


be 
Or 


one open. In still lower, the outer is closed and the inner is used. 
Or, these several dispositions are made not in accordance with the 
stage of the stream, but with the requirements of the mill. 

This arrangement has the advantage that it fixes three different 
quantities of water which can be used with good effect, instead of one 
























































































| a 
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Penstock || mill 
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Draft-tube 


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43 


SS 
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ZZZZZZLE 


Fig 17 


as in the ordinary case. Any quantity between the capacity of both 
wheels and the capacity of the small wheel can be used with little 
loss. Below the latter quantity the defect appears in full force. The 
form of bucket adopted in this wheel, although of good efficiency at 
full gate, is one of the worst forms extant at part gate. However 
small the quantity of water admitted to the wheel, it is certain 
to issue in a uniform stream from the orifices of discharge with 


26 A More Perfect Form of Water - Wheel. 


greatly diminished velocity. This wheel is also liable to losses from 
which ordinary types are exempt. A turbine, in order to give its 
best effect, must run with a velocity which bears a certain ratio to 
that due the head. The connections must be such as to admit of this 
velocity when the shafting and machinery run at their normal speed. 
Two wheels of different diameter on the same shaft, cannot both run 
at this velocity. Moreover the wheel out of action is kept in rotation 
as a useless drag upon the other. 





Fig. 18 


5. In the forms of wheel shown in Figures 18 and 19, the guide 
serves the double purpose of guide and gate. It controls the width 
of the guide passages by turning upon a hinge or joint under the action 
of the regulator. In 18, the outer end of the guide is fixed; the 
inner end is susceptible of an outward movement, limited by the 
adjoining guide. In 19, the inner end is jointed, the outer end 
rotates. The passages are closed when each guide touches the 
adjoining guide. 

The same remark may be made of this arrangement as of the 
Swain wheel. It obviates the loss incident to a change of direction 
and velocity of the eiftering water. But it in no way affects the 
second source of loss, viz. that arising from the expansion of the 


~l 


A More Perfect Form of Water - Wheel. 2 


stream in the wheel passages. To avoid this latter loss would require 
the wheel passages to be contracted in the same proportion as the 
guide passages, when the discharge is reduced. 

From this brief survey of the present state of the art of wheel- 
building we are, I think, justified in asserting that no existing form 
of wheel is free from grave, inherent and unavoidable defects, defects 
which are material at full discharge, and become more and more 
marked as the discharge diminishes. No existing form is consistent 





in design with the highest degree of efficiency or with the well estab- 
lished principles of hydraulics. 

They have resulted from tentative methods and from partial and 
incomplete knowledge, not from a thorough and comprehensive 
study of the whole subject. 

It appears to me, also, that the only hope of developing a perfect 
water-wheel lies in a radical departure from existing forms, every one 
of which is intrinsically defective. 

The whole subject of improvement turns upon this question: Are 
the guides necessary and indispensable to the efficient action of the 
wheel? Iam convinced that they are not. It appears to me that in 
a wheel surrounded by a free space sufficient to allow the water to 


28 A More Perfect Form of Water - Wheel. 


move without constraint, it would naturally take the direction and 
velocity most conducive to the efficient action of the wheel. ‘This, in 
a center-vent wheel, means a velocity, the tangential component of 
which is equal to the velocity of the exterior circumference of the 
wheel. What reason have we for supposing that the water will take 
that velocity’?* We have the very simple and satisfactory reason 
that the water cannot otherwise enter the wheel. ‘This answer, how- 
ever, carries another question with it, viz.: Though there is no doubt 
that the water would take the required velocity, would not that move; 
meut be attended with serious loss of energy? I think not, for these 
reasons : — 


K 





Fig. 2O 


1. When an orifice is opened for the escape of water under press- 
ure, the water will approach the orifice. If the orifice recedes, the 
water will follow and overtake it. 

2. A movement of rotation, under the conditions supposed, is in 
accordance with the natural tendency of the water. Water in a cir- 
cular vessel, discharging through a central orifice, spontaneously 
takes a movement of rotation.+ 

* This would be true for an orifice opening normally, as 7, Fig. 20, or backwards, as 
atk. It would not be true for an orifice opening toward the direction of rotation, as @. 
In that case, tle water would be “ scooped” into the wheel without taking the full ve- 
locity of the wheel. 

+ When a heavy particle (i.e. a particle having weight) moves freely under the action 


of a force directed toward a fixed point, the line joining it with the fixed point describes 
equal areas in equal times. This general proposition appears from Fig. 21. Suppose a 


A More Perfect Form of Water - Wheel. 29 


3. It is a universal principle of nature that every movement is 
performed with the minimum expenditure of energy. Water, in the 
case supposed, will enter the orifices of the wheel with the least loss 
of energy possible under the existing conditions. Now we know 
that if the water reaches the orifice with the rotatory velocity of the 
wheel, the loss of energy will be slight; and since we know that ex- 
isting conditions admit of this velocity, and that the actual loss will 
be as small as is consistent with existing conditions, we are entitled 
to assume that the actual loss will be slight. 

4. If we assume that the water enters the wheel with a less ve- 
locity than that of the floats, and suddenly acquires the motion of 
the latter, this sudden accession of velocity does not necessarily im- 
ply any loss of energy. Loss of energy may occur in several ways. 





D Cc B A 


Fig. ra | 


heavy particle to move with uniform velocity.in the line A D,— A B, BC, CD, being 
the equal distances moved in successive elements of time. Let O be any point whatever. 
The triangles A OL, BOC, COD, are the areas described in equal times with reference 
to 0. These triangles are all equal to each other, having equal bases and the common 
height A H = the perpendicular distance of O from A D. 

Now introduce the supposition that, at @, the particle is acted on by a force directed 
toward QO, which would cause it to move a distance ( / in the element of time. At D 
draw DG, parallel to CO, and on it lay off DE=CF. Draw CE, then C EO is the 
area described in the element of time under consideration. Join E O, and draw OG, 
perpendicular to DG. The triangle C DZ = O D £, both having the base D /, and the 
common altitude 0G. 

The triangle CH O=CDO—(CDE—DKE)+O0DE—DKE=CDO. There- 
fore, the areas described in successive elements of time are equal; and in order to make 
these areas equal, the velocity must increase as the particle approaches the fixed point. 
This is the law discovered by Kepler, and it governs the motions of the planets. 

A particle of water in the wheel-case is under conditions very similar to those of a 
planet in free space. It enters the case with a certain velocity. As soon as it enters, it 
is acted on by a force directed toward a fixed point, i.e. the center of the wheel. It 
does not move straight toward the wheel, but circles around it with an increasing 


velocity. 


30 A More Perfect Form of Water- Wheel. 


One of these is the communication to the water of motions other 
than those necessary for its entrance into the wheel, i.e. useless 
movements. Commotions in water commonly arise from irregulari- 
ties in the channels, or in the circumstances of movement. No such 
irregularity exists here. Loss of energy occurs when water passes 
orifices with contraction. No appreciable loss can occur here from 
that cause. ‘The contraction, if any, is only that due to the radial 
component of the velocity, which is not over one-fifth of the tangen- 
tial component. Each orifice of entrance has the contraction sup- 
pressed on one side, and it is rounded on two others. On the fourth 
side, contraction can only exist in virtue of the excess of the wheel’s 
velocity over the tangential component of the water’s velocity. Nei- 
ther contraction nor commotion therefore can exist as a source of 
serious loss. 

The most natural conception of the phenomenon is this: The water 
which has passed the tips of the floats is in motion with the full ve- 
locity of the wheel, the next outside film a little slower, the next 
slower still, etc., the acceleration being communicated by fluid fric- 
tion. The loss of energy consists in the fact that, of two consecu- 
tive films of water, the one nearest the wheel moves a little faster 
than the one more remote, so that the energy expended is not fully 
represented by the velocity acquired. ‘The energy represented by 
the velocity imparted to the film of water is not lost. 

The loss, however, from fluid friction in this wheel is no greater 
than in any wheel of equal surface (speaking now of the general 
surface of the wheel, not that containing the orifices) and equal 
velocity. In any wheel, the film in contact with the wheel moves 
with the velocity of the wheel, the adjoining film a little slower, the 
next slower still, etc., precisely as in this. 

I have, therefore, become convinced that the guides, although in 
existing forms of wheel, necessary for constructive reasons, are in 
no sense essential to the efficient action of the wheel. That they are 
attempts to force upon the water a direction and velocity which it 
would take spontaneously if relieved of constraint. That, ordina- 
rily, they but imperfectly fulfill their purpose at full gate, and are a 
prolific source of waste at part gate. The first step in the improve- 
ment of the water-wheel, therefore, is, as it appears to me, to dis- 
pense with the guides, and to adopt a form of wheel that does not 
require them for constructive reasons. 

The second essential to the perfect action of the water is a gate 


9 


A More Perfect Form of Water - Wheel. 31 






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that shall, in closing, contract not only the influx of the wheel, but 


the entire passages through it. 


The attainment of these conditions necessitates an abrupt and 


radical departure from all existing forms of water-wheel. 


The figures which follow illustrate my idea of a form of water- 
It must 


wheel calculated to obviate all the above described defects. 


fect Form of Water - Wheel. 


ev 


A More Per 


SSSR AS AAAS anennnnnnnn ny //74 


COSSSSUS SSSI SG 








aioe 





























v2 








shaft 


on horizontal 


No 2 


Wheel 
Sectional plan- half, looking up, and half. looking down. 


Fig. £3 


A More Perfect Form of Water - Wheel. 33 


be observed that these are, in no sense, working drawings. They 
are intended to exhibit the principles on which such a wheel could be 
constructed, and are sufficiently detailed to show that the construc- 
tion of such a wheel involves no mechanical impossibility, and is 
entirely within the resources of modern engineering. 

Fig. 25 shows the form of the floats and float passages, Figs. 22 
and 23 the form of the gate. The gate g is a conoidal dise with a 
central hub, which slides on the shaft. A heavy hub, secured to the 
shaft, carries the flat dise or discs dd, to which the floats f are se- 





Wheel Na2 .on horizontal 
shaft 


Elevation, 
Fig. a4 


cured. ‘The outer part of the gate is provided with openings through 
which the floats pass. ‘These openings admit of being packed as in- 
dicated at Fig. 28. Stout rims are attached to the outer ends of the 
floats in the manner to be described later. ‘The water approaches 
the wheel from the exterior with a revolving motion. Its rotatory 
velocity at its entrance to the wheel is equal to the velocity of the 
exterior circumference. If this was not so, the water would not 
enter the weeel. It is discharged in the reverse direction with a 
velocity nearly equal to that due the head. Its entrance to the mov- 
ing orifices of the wheel implies no greater shock or loss of head 
than would be involved in its entrance to rounded stationary orifices. 
It passes the wheel under conditions consistent with maximum efli- 
ciency. These conditions are in no way changed by the opening or 
closing of the gate. ‘The energy of the water in this wheel is devel- 
oped wholly by reaction. It is, as shown at page 10, nearly double 


34 A More Perfect Form of Water - Wheel. 


fe 
y 
y 
; 







on y y of fig 22 


Fig. 25 


Section 


m of Water - Wheel. 


A More Perfect For 


LA oe: 





is 


Fig. &6 


36 


A More Perfect Form of Water - Wheel. 


Pn ss 
eT 
~ 


~ 





ei 





y fO X-X UO UO!LI—aS 





gee 
=- 
= 
- - 
- — 


a 
- 


but half of this energy | 


2 the whirling movement to the 


) 


that due to the head and quantity of water ; 


is absorbed in the work of impartin 


water before or during its entrance to the wheel. 


A More Perfect Form of Water - Wheel. 37 


We will now describe the construction of the wheel and its ad- 
juncts. Figs. 22 to 28 relate to a wheel on a horizontal shaft. 

The Gate is in two parts: — The first part is a dise of conoidal 
shape which slides horizontally upon the shaft; the second is a cylin- 
der with a broad internal flange, as shown at Fig. 28. Both parts are 
pierced with openings for the passage of the floats. At the junction 
of the two parts is a thick sheet of fibrous packing, pierced in like 
manner. ‘This being compressed by the screws which fasten the two 
parts together packs the floats. The cylindrical part of the gate has 
the packing ring 7, so that, in a single wheel, the space between the 
gate and disc, in a double wheel the space between the two gates, 
becomes a water-tight compartment. It would be a very simple 
matter, also, to introduce packing at the hub where it slides on the 
shaft. 

The Discs. — The wheel under consideration is a double wheel. 
The central hub which is fastened to the shaft carries two flat circular 
discs. These have openings, 0, which allow the water to pass freely. 
The rim of the dise is thickened and notched like a ratchet wheel, 
as shown at Fig. 27. 

The Floats. —'These are continuous through both wheels. The 
part traversed by the gate is of the form shown in section, Fig. 25. 
The part resting on the dises, and lying between them, has the sec- 
tion shown by the cross natching in Fig. 27, the blade of the float 
coming to a close shoulder against the disc, and preventing any ten- 
dency to endlong displacement. After being put in place and tem- 
porarily fastened, the wheel is put in a lathe, and the central part of 
the floats turned off smoothly, leaving the diameter of that part of 
the wheel a little greater than that of the outer ends of the floats. 
Then a heavy band, B, isshrunk on. Fig. 28 shows this band extend- 
ing oyer the whole space covered by the discs, but two narrower 
bands would do as well. The float may have a thickness of 14 inches 





near its outer edge, forming a very strong stiff bar. The outer end 
of the float is turned down to a cylindrical stud, 14 inches diameter, 
and 14 inches long, and threaded. Some 4 of the floats in a wheel 
are bored longitudinally with holes, 0, Figures 25, 26 and 28. These 
holes reach from the outer end to the disc, and are there met by holes 
cut from the outside of the float. These holes connect the interior 
of the wheel with the low pressure compartment of the case. The 
band, B, is thicker at one disc than the other to allow the cylindrical 
parts of the gates to telescope when open. A groove is turned in 


38 A More Perfect Form of Water - Wheel. 


the band, at each disc, for the packing ring 7. After shrinking on 
and finishing the bands, the cylindrical part of the gate is put on, the 
flange straddling the floats. Then the sheet of fibrous packing is 
slipped on. Then the discoidal part of the gate is adjusted, and the 
screws turned up which connect the two parts and compress the 


= N 
SS 
LikiiiiiiiiiiiDieliisidiiViidildllldlde 


< \ : : By , 


yy 
ei 























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Wiss 


SSN 


FY 
Se 


Section on k-kK of fig 27 


Fig. 28 


packing. Then the rim, which is bored to receive the threaded studs 
on the outer ends of the floats, is put in place and solidly fastened 
by countersunk nuts. ; 

The Shaft has an internal bore-hole communicating with the inte- 
rior of the wheel. At the end of the shaft this bore-hole communicates 
with a pipe by a stuffing-box. 


A More Perfect Form of Wuter - Wheel. 39 





The Case. — The wheel being set above the level of the canal of 
discharge, the case has high pressure and low pressure compartments. 
The case is shown in Figures 22, 23 and 24. It is a short cylinder of 
cast iron with flanges for the attachment of the penstock and draft 
tubes. The interior compartment is in communication, by means of 
the penstock, with the upper level of the mill site. Being exposed to 
a bursting pressure, it is formed by two conical diaphragms joining 
the large cylinder. The junction is marked by two broad ribs run- 
ning around the latter and widening into flanges for the attachment 
of the penstock and draft tubes. An annular portion of these dia- 
phragms, next the wheel, is made detachable for convenience of fin- 
ishing. Ribs also run around the ends of the exterior cylinder, and 
expand into flanges for the attachment of the draft tubes. The pres- 
sure on the ends of the cylinder is inward, and these ends are of dish 
shape, bending inward. ‘This form not only gives great strength to 
resist the pressure, but shortens the unsupported part of the shaft. 
The flattened portion of the penstock, at its junction with the case, 
can be strengthened by external ribs, if required. ‘The draft tubes 
being rectangular in section are divided by partitions into several dis- 
tinct passages, as shown in Fig. 24, for greater strength. As the 
rim w, of the wheel, Fig. 26, must revolve without touching the case 
c, an annular space must exist, allowing for wear and imperfection 
of workmanship, through which the escape of water would be objec- 
tionable. To alleviate this difficulty, the small ring, 7, is confined 
to a seat turned on the case so as to be capable of slight lateral 
movement. This ring can fit the rim of the wheel much closer than 
the fixed case, while yielding to any slight displacement of the wheel, 
from wear or other cause. 

The Bearing, }, of the shaft, is an undivided cylinder. It has a rib 
or flange around the middle by which it is riveted to a circular plate 
of wrought iron. This latter is fastened, at its outer circumference, 
to the end plate of the case, covering a circular opening in the same, 
some 30 or 36 inches in diameter. The bearing has an oil-cup and 
a packing gland not shown. This bearing, I presume, will be the 
subject of some criticism, but I think it a correct design. Bearings 
are usually made in two halves, for convenience ih setting up machin- 
ery rather than any inherent advantage in that method. The ring of 
boiler plate surrounding the bearing gives it a slight but sufficient 
degree of flexibility, which is favorable to uniform wear. The press- 
ure being from without inward favors the admission of oil. The 





40 A More Perfect Form of Water - Wheel. 


admission of water to a bearing which is well lubricated is no disad- 
vantage, as is shown in the Westinghouse engine, where the bearings ~ 
run constantly in water covered with oil. 

Regulation. — Fig. 29 is a schematic sketch of the proposed regu- 
lator, and Fig. 380, a section of the valve for controlling the move- 
ment of water through the central bore-hole in the shaft. The plug 
of the valve carries an arm resting on the spindle of the regulator, 





Lib 


med LDL if 4 
Sa 


Je 


Sketch of governor and 
section of valve to regulate 
Speed of wheel—— 


and weighted as indicated, so that it follows the movement of the 
spindle, under the action of the revolving balls, rising when the 
speed diminishes, and falling when it increases. An increase of 
speed opens the passage leading from the upper level to the wheel; 
a decrease closes it. Now, in the normal running of the wheel, 
water is escaping from the closed chamber through the small orifices 
o, in the floats, and entering through the valve. When the valve opens 
wider, an increased quantity of water enters the chamber, raises the 
pressure therein and moves the gate to close. When the speed sud- 






A More Perfect Form of Water - Wheel. 41 


denly starts forward, the valve opens wide and closes the gate rapidly. 
When the valve closes to less than the normal opening, water escapes 
faster than it enters, the pressure in the chamber falls below that in 
the low pressure compartment, and the gate opens. The rapidity with 
which the gate will open when the valve is entirely closed will depend 
on the size and number of the openings 0, that is, upon the quantity 
of water constantly wasted. ‘The wheel under consideration has an 
external diameter of 5 feet and is supposed to draw some 200 eubic 
feet of water per second, 12,000 per minute, under a head of 20 feet. 
The cross-section of the closed chambers may be taken at 20 square 
feet. To move the gate at the rate of 12 inches in a minute would 
involve a loss of 20 cubic feet per minute, which in comparison with 
12,000 is not worth considering. A movement at the rate of 12 
inches per minute would suffice for any ordinary use of a water- 
wheel. A closing movement of any desired rapidity can be attained 
by suitable proportions of valves and passages without waste of 
water. To start the wheel from rest, the weighted arm is thrown 
into the position ‘* to start,” Fig. 29. Then the interior of the wheel 
is in communication with the lower level, and water from the upper 
level rushes through the nozzle into the pipe leading to the lower 
level, forming a jet pump which draws the water or air from the in- 
terior of the wheel, and opens the gate. ‘To stop, when running, the 
weighted lever is thrown into the position marked ‘‘ to stop.” Then 
the valve is free from control of the regulator, and the interior of the 
wheel is in full communication with the upper level; the gate closes. 
On a low head it might be doubtful whether the wheel could be 
started with certainty by this method. In that case it might be ad- 
visable to temporarily connect the pipe ‘‘to upper level,” with a 
municipal water-main, or with the fire-tank of the mill, which would, 
if required, make a complete vacuum in the wheel chamber. In start- 
ing the wheel after the water has been shut out of the penstock, the 
draft tubes and wheel chamber would be filled with air. The latter 
would remain filled with air after the starting of the wheel, and, as it 
filled with water, the air would collect at the center and obstruct the 
regulation of the wheel. In this case the gate would be opened far 
enough to admit a large volume of water and expel the air from the 
draft tubes, raising the water in the latter above the wheel. ‘Then 
admit water from the upper level, close the gate and expel the air, 
which escapes through the highest orifices 0. Then the gate can be 
opened without admitting air. Of course the air can be drawn out 


« 


ct Form of Water - Wheel. 


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A More Perfect Form of Water - Wheel. 43 


‘ 


by the jet pump, but this would involve opening the gate to its full 
width, which might not be desirable. 

Equations 11 to 15 were deduced with reference to the regulation 
of the wheel by the action of centrifugal force. We will inquire 
what amount of force we have at disposal for the movement of the 
gate. ‘The wheel under discussion is 5 feet in diameter on a head of 
20 feet. This wheel takes a higher velocity than one of the common 
form, in which the head is partly expended in imparting the velocity 
through the guide passages. The exterior circumference would move 





Wheel on vertical shaft-— Plan 


Fig. 32. 


_ with very near the velocity due the head. When the influx of water 
to the wheel chamber is shut off, the internal pressure at the cireum- 
ference is equal to the external pressure at the center. The internal 
pressure at the center is less than this by the head due the velocity, 
which we may call the centrifugal head. This head, in the present 
case, would not be less than 16 feet. The force tending to open the 
gate is equal to 8 feet depth of water acting on a surface of some 20 
square feet — over 10,000 pounds. The force to be overcome is the 
friction due to the weight and packing — nothing approaching the 
above. Consider the most unfavorable case that could occur, 12 
feet may be taken as the lowest head that a horizontal wheel would 
be used on, and 36’/’ diameter would be about as small a wheel as 
would be used on such a head. The centrifugal head would not be 
less than 10 feet. The pressure tending to open the gate is, roughly, 


fect Form of Wuter- Wheel. 


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A More Perfect Form of Water - Wheel. 45 


yx 38x 3 XK 7854 XX 62.5 = 2209 lbs. For a head less than 12 
feet we should employ a wheel on a yertical shaft. 6 feet may be 
regarded as the lowest head worth developing by water-wheels. On 
such a head there is seldom occasion to use a small wheel. » A 5-ft. 
wheel on a 6-ft. head would expose to pressure something over 
20 square feet for moving the gate. The centrifugal head would 
be about five feet. The pressure would amount to about 20 K 25 x 
62.5= 3125 lbs. Of course we may conceive of a head so low and 
a wheel so small that this mode of regulation would be inapplicable. 
To meet such causes I am prepared to say that a regulator may 





Single wheel on vertical shaft 
Plan. 


Fig. 34 


be devised capable of creating a total or partial vacuum within the 
wheel chamber. 

There is never any question as to the amount of force available for 
closing the gate. With full communication between the wheel 
chamber and the upper level, the water enters the former much 
faster than it can be discharged. The centrifugal head acts in con- 
cert with the static head to close the gate. 

In every application of this method, the water issuing from the 
floats changes its direction by a right angle in leaving the wheel. 
This change of direction causes a pressure on the gate tending 
to open it. The water should not leave the wheel with a velocity of 
more than 6 or 7 feet per second. With 7 feet at full gate, the 
pressure would amount to a head of some 15 inches, diminishing to 


46 AW More Perfect Form of Water - Wheel. 


nothing as the gate closes. No reliance can be placed on this force 
as aiding the opening of the gate. ; | 

The foregoing description contemplates a wheel on a horizontal 
shaft. Figures 31-2-3-4 show that the proposed construction is just 
as applicable to a wheel on a vertical shaft; 31-2 show a double 
wheel; 33-4 a single wheel. Neither of these presents any peculiar 
difficulty, or requires any special description. For a small quantity 
of water on a low head, a single wheel would be preferable to a 
double one of smaller diameter. In such case it would probably be 
better to let the wheel discharge upward instead of downward as 
indicated, in order that the weight of the gate might assist in open- 
ing. 

Wheels often run under conditions to which the foregoing mode of 
regulation is inapplicable, as, for instance, in connection with a 
steam-engine, which controls the speed, and meets all variations in 
the demand for power. In this case, the wheel, when under no 
limitation as to quantity of water, runs at full gate, the regulator 
disconnected, and the valve set to keep the gate open. Sometimes, 
however, the wheel is under limitations as to the quantity of water. 
Natural limitations resulting from diminished flow of the stream. 
Legal limitation of leases and grants. In such case the gate cannot 
be set at any unalterable opening. It can only be left in control of 
the valve. It is obvious that the latter must be controlled by condi- 
tions other than the speed of the wheel. 

It would be easy to point out modes of regulating the discharge, 
without reference to the velocity, to conform to the varying flow of a 
stream, to a uniform draft of water or to a uniform output of power. 
But such inquiries would carry us far beyond the contemplated limits 
of this paper. 











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